Abstract
In a normed space we introduce an exact and approximate orthogonality relation. We consider classes of linear mappings approximately preserving this kind of orthogonality. We show that, in particular, the property that a linear mapping approximately preserves the $B$-orthogonality is equivalent to that it approximately preserves the $\rho,\rho_+$-orthogonality (although these orthogonalities need not be equivalent). Moreover, we show that every approximately orthogonality preserving linear mapping is necessarily a scalar multiple of an almost isometry.
Citation
Paweł Wójcik . "Linear mappings approximately preserving orthogonality in real normed spaces." Banach J. Math. Anal. 9 (2) 134 - 141, 2015. https://doi.org/10.15352/bjma/09-2-11
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